首页|Risk Models for the Prize Collecting Steiner Tree Problems with Interval Data

Risk Models for the Prize Collecting Steiner Tree Problems with Interval Data

扫码查看
原文链接
  • NETL
  • NSTL
  • 万方数据
  • 维普
Given a connected graph G =(V,E) with a nonnegative cost on each edge in E,a nonnegative prize at each vertex in V,and a target set V' (∈) V,the Prize Collecting Steiner Tree (PCST) problem is to find a tree T in G interconnecting all vertices of V' such that the total cost on edges in T minus the total prize at vertices in T is minimized.The PCST problem appears frequently in practice of operations research.While the problem is NP-hard in general,it is polynomial-time solvable when graphs G are restricted to series-parallel graphs.In this paper,we study the PCST problem with interval costs and prizes,where edge e could be included in T by paying cost xe ∈ [ce-,ce+] while taking risk (c+e-xe)/(ce+-ce-) of malfunction at e,and vertex v could be asked for giving a prize yv ∈ [pv-,pv+] for its inclusion in T while taking risk (yv-pv-)/(pv+-pv-) of refusal by v.We establish two risk models for the PCST problem with interval data.Under given budget upper bound on constructing tree T,one model aims at minimizing the maximum risk over edges and vertices in T and the other aims at minimizing the sum of risks over edges and vertices in T.We propose strongly polynomial-time algorithms solving these problems on series-parallel graphs to optimality.Our study shows that the risk models proposed have advantages over the existing robust optimization model,which often yields NP-hard problems even if the original optimization problems are polynomial-time solvable.

uncertainty modelingprize collecting Steiner treeinterval dataseries-parallel graphspolynomial-time solvability

Eduardo (A)lvarez-Miranda、Alfredo Candia-Véjar、Xu-jin CHEN、Xiao-dong HU、Bi LI

展开 >

Industrial Management Department, Universidad de Talca, Chile

DEI, University of Bologna, Italy

Academy of Mathematics and Systems Science, CAS, Beijing 100190, China

National Natural Science Foundation of China973 Program of ChinaChinese Academy of Sciences"Center for Research and Applications in Plasma Physics and Pulsed Power TechnologyDirección de Programas de Investigación,Universidad de Talca,Chile

11021161 and 109281022011CB80800kjcx-yw-s7PBCT-Chile-ACT 26"

2014

10.1007/s10255-014-0269-z

应用数学学报(英文版)
中国科学院应用数学研究所 中国数学会

应用数学学报(英文版)

CSTPCDCSCDSCI
影响因子：0.149
ISSN：0168-9673
年,卷(期)：2014.30(1)
  • 33